The USA had the luxury of being the only major combatant that had no fighting on its domestic territory. As such the USA was able to mobilize its huge resources and economy and thus produce more armaments than any other nation.
By the end of the war the USA had created the largest naval force and air force in world history. Again, not being directly attacked, the USA never developed a major fighting army as compared to Germany or Russia or even France. The USA army was involved in significant fighting in a few rather limited engagements such as North Africa (performed poorly), Sicily and Italy (better performance but nothing dramatic, just a long attrition battle), North France (performed adequately against second rate, immobile German troops), and Belgium (poor performance in the Battle of the Bulge), and Germany proper (lop sided battles against immobile, demoralized, cut off German troops). Late in the war, the USA army engaged some Japanese forces in battle, such as at Okinawa. IMO the USA army was never really tested in WWII against a major, well armed foe. By the time the USA got into Europe the Germans had no air cover and very limited mobility. It is a miracle Germany did not collapse more quickly, say late 1944.
The USA Marine corp performed exceptionally in WWII, virtually defining the amphibious assault for the war.
IMO the USA air force performed much better than any similar force on earth during 1943-45. Unlike the British, the American AF took on the German defences during daylight and the bombers generally sought out military targets. The British in contrast gave up on day light bombing (until late in the war) preferring the easier process of targeting civilians for bombing at night.
The USA naval forces were nothing short of phenomenal. Outnumbered in numerous battles the USA forces nonetheless won almost every engagement against well run, well equipped Japanese forces. The USA submarine battles against Japan were also exceptional.
Overall you could say that the USA did about 90% of the fighting for the Allies in the Pacific (combined naval, air and land). Against Germany the USA did about 45% of the air campaign, 10% of the land campaign, and probably 5% of the naval.
Other than direct fighting the USA produced vast amounts of food, arms and other goods for its allies. Huge amounts of goods were shipped to Russia, China, Britain and others. Britain relied almost entirely on American loans and oil to stay in the war after 1940. Russia relied largely on American trucks, boots and food to keep their armies mobile after early 1943.
In summary it is unlikely the allies could have defeated Germany in a conventional war without American help. Likely the war would have ground down to a stalemate by 1944 with Germany still along the English Channel, controlling Italy and probably somewhere around Odessa/Minsk/Riga in Russia. The Pacific war was a hopeless cause for Japan and even a major victory such as Midway would not have saved Japan.
The fact is the Germans were the best at warfare just like every other army that faced them we had to learn the hard way and got our butts kicked at Kasserine. The Germans however were stopped short of their goals by some very tough fighting US GI's. They fought fiercely in Tunesia and in Sicily stole the show from the British where they performed brilliantly. I give them an A+ for the D day landings certainly at Omaha and how they held together in the bocage fighting that was more like WWI. The terrain in Italy was awful and the Germans there were the best I doubt that the Russians would have done any better there. AS far as Anzio I agree with digging in and waiting for the German counter attack rather than marching on Rome as it was the USA Naval guns played a vital role in stopping the German attack what might of happened if we were all spread out from the beach to Rome.
